Yes, you can. The police search vehicles, homes, other areas illegally all the time. They do it without a warrant.
They're supposed to have a warrant, so it's important that you talk to an attorney early on so that you know whether or not it's one of the instances where they can search without a warrant.
We see it all the time, and cases, entire cases, evidence is subject to being suppressed, and the case dismissed. Definitely look into this with your attorney.